The displacement of a particle performing S.H.M is given by $x=5 \sin (3 t+3)$, where $x$ is in…

The displacement of a particle performing S.H.M is given by $x=5 \sin (3 t+3)$, where $x$ is in $\mathrm{cm}$ and $t$ is in second. The maximum acceleration of the particle will be
  1. $15 \mathrm{~cm} \mathrm{~s}^{-2}$
  2. $30 \mathrm{~cm} \mathrm{~s}^{-2}$
  3. $45 \mathrm{~cm} \mathrm{~s}^{-2}$
  4. $90 \mathrm{~cm} \mathrm{~s}^{-2}$

Solution

$x=5 \sin (3 t+3)$ Standard equation of S.H.M. is $x=A \sin (\omega t+\alpha)$ $\therefore \mathrm{A}=5 \mathrm{~cm}, \omega=3 \mathrm{rad} / \mathrm{s}$ Maximum acceleration $\mathrm{a}_{\mathrm{m}}=\mathrm{A} \omega^2=5 \times(3)^2$ $=5 \times 9=45 \mathrm{~cm} \mathrm{~s}^{-2}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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